Electronic and Magnetic Properties of FeCl₃ Intercalated Bilayer Graphene

Abstract

Graphene has gained significant attention since its discovery in 2004, and the modification of few-layer graphene provides a platform to tailor its physical and electronic properties. In this study, we employed unrestricted density functional theory (DFT) with the PBE+U functional to investigate the electronic and magnetic properties of FeCl₃-intercalated bilayer graphene (BLG). Both in BLG and stage-2 intercalated graphite, a distinct localization of electrons on a specific Fe atom is evident, gaining approximately 0.245 electrons evaluated with Bader analysis, while the holes are delocalized within the graphene layers. This results in p-doped graphene, characterized by a shift of the Dirac cone by 0.74 eV for BLG and 0.70 eV for stage-2 intercalated graphite. Ferromagnetic ordering is observed within the plane of FeCl₃-intercalated BLG, whereas the FeCl₃ layers exhibit antiferromagnetic coupling in stage-2 intercalated graphite. The ferromagnetic nature and electronic structure of the FeCl₃-intercalated BLG is retained under pressure.

1. Introduction

Graphite intercalation compounds (GICs) [1,2] have attracted considerable attention due to their distinct properties arising from the introduction of intercalants into graphite host materials [3,4]. These intercalants encompass a range of materials, including well-known alkali and earth metals, as well as metal oxides, metal chlorides, acidic oxides, fluorides, and oxyhalides [5,6,7]. Since the concept of GICs was first introduced in 1841, these compounds have been extensively studied [8] and characterized using diverse methods. The unique structural, magnetic, electronic, and optical properties of GICs have paved the way for their applications in various fields, including electrodes in batteries, fuel cells, and catalysis [9].

On the other hand, a monolayer of graphite, called graphene [10], has gained significant attention due to its remarkable properties and the presence of Dirac fermion-like charge carriers [11]. In recent years, substantial progress has been made in graphene research, and various methods [12,13] have been explored to customize its electronic and structural characteristics. Due to the high surface-to-bulk ratio inherent in two-dimensional systems, few-layer graphene (FLG) intercalcation offers opportunities to explore novel chemical and physical phenomena [14,15,16,17]. Unlike bulk GICs, FLG exhibits unique properties [18] due to the presence of surface boundaries, which disrupt the translational symmetry perpendicular to the graphene layers. By hybridizing FLG with other molecules through chemical or physical reactions, the properties of FLG can be tailored and utilized in various applications [19,20]. Among the FLG family, bilayer graphene (BLG) intercalation compounds have garnered particular interest due to their diverse magnetic and superconducting properties, providing a platform to investigate long-range ordered phenomena in two-dimensional systems [21,22].

Intercalant FeCl₃ [23] stands out from many other GICs due to its relative stability in open-air environments, which has attracted continuous research interest [24,25]. A Hall bar device [26] utilizing FeCl₃-intercalated graphite has been successfully fabricated, demonstrating a high carrier density exceeding 10${}^{13}$ cm${}^{-2}$, indicating its potential for environmentally stable utilization as electrical conductor. The strong charge transfer effect between the carbon atomic layers and FeCl₃ significantly modifies the band structure of graphite, resulting in p-type doping for different stages of intercalation [27,28]. Zhan et al. successfully prepared FeCl₃ intercalated few-layer graphene (FLG) using a two-zone vapor transport method [29]. Despite the potential applications of FeCl₃-intercalated bilayer graphene [30], comprehensive research on its magnetic and electronic properties is scarce. Gaining a thorough understanding of these properties is essential, as it can provide valuable insights into the potential applications of this system. Li et al. [31] investigated the structural, electronic, and magnetic properties of stage-1 and -2 FeCl₃-based GICs in the framework of the GGA+U implementation of DFT. By applying the experimental lattice parameters, their calculation results are in agreement with the experimental findings, in which stage-1 shows antiferromagnetic ordering below 3.6 K and stage-2 displays ferromagnetic ordering below 8.5 K [7]. Kim et al. [26] investigated the electronic properties of FeCl₃-intercalated BLG using the fixed interlayer distance of the value of bulk GIC, 0.94 nm. Their DFT+U calculations predict the Fermi level shift of around 0.6 eV and charge transfer of around 0.01 eV per C atom. However, there is no prior research that has conducted a full optimization of lattice parameters and structures while considering the influence of the dispersion interactions.

In this study, we want to extend the already existing first-principles calculations to investigate the magnetic and electronic properties of FeCl₃-intercalated BLG with different stacking patterns. The calculations were performed using the unrestricted PBE+U functional, and dispersion interactions were considered. Our results reveal that both in BLG and stage-2 intercalated graphite, a distinct localization of electrons on a specific Fe atom is evident, gaining approximately 0.245 electrons, while the holes are delocalized within the graphene layers. Moreover, we have explored the effect of uniaxial pressure applied perpendicular to the two-dimensional (2D) system on the magnetic states and electronic properties of FeCl₃-intercalated BLG.

2. Computational Detail

The spin-polarized DFT calculations based on plane-wave basis sets were performed with the Vienna $ab$ $initio$ simulation package (VASP) [32,33]. The Perdew–Burke–Ernzerhof (PBE) exchange-correlation functional [34] was employed. The ion-cores were described by projector-augmented-wave (PAW) potentials [35] and the valence electrons (Fe ($3d$, $4s$), Cl ($3s$, $3p$) and C ($2s$, $2p$)) were described by plane waves associated with kinetic energies of up to 500 eV. Brillouin-zone integration was performed on $\mathrm{\Gamma }$-centered symmetry with Monkhorst-Pack meshes by the tetrahedron method with Blöchl corrections [36]. The $3\times 3\times 1$ k-mesh was used for the structure optimization. The DFT+$U$ scheme [37,38] was adopted for the treatment of Fe $3d$ orbitals, with the parameter $U_{\mathrm{eff}}=U-J$ equal to 4 eV [31]. Dispersion interactions were considered by Grimme’s D3 parameterisation [39]. The charges of individual atoms are calculated by performing Bader charge analysis [40].

When modeling the FeCl${}_3$-intercalated BLG, a supercell with $5\times 5$ units of graphene hexagonal primitive cell and $2\times 2$ units of one layered FeCl${}_3$ primitive cell ($\overline{R}$3 space group) was constructed. A vacuum gap was set to approximately 30 Å. During structure optimization, the convergence criteria for energy and force were set equal to ${10}^{-5}$ eV and ${10}^{-2}$ eV/Å, respectively. Phonon calculations were performed at the gamma point, showing that the FeCl${}_3$ structure yields only positive frequencies. This result indicates the structural stability of intercalated FeCl${}_3$.

The binding energy of FeCl${}_3$-intercalated BLG system is defined as follows:

$$\Delta E_{\mathrm{bind}}=E_{\mathrm{total}}-E_{{\mathrm{FeCl}}_3}-E_{\mathrm{BLG}},$$

(1)

where $E_{total}$ represents the total energy of the FeCl${}_3$-intercalated BLG system, $E_{{\mathrm{FeCl}}_3}$ is the total energy of the $2\times 2$ units of one-layer FeCl${}_3$ primitive cell, and $E_{\mathrm{BLG}}$ is the total energy of $5\times 5$ units of AA or AB stacking BLG.

The intercalation energy of stage-2 GICs system is defined as follows:

$$\Delta E_{\mathrm{int}}=E_{\mathrm{total}}-E_{{\mathrm{FeCl}}_3}-E_{\mathrm{graphite}},$$

(2)

where $E_{total}$ represents the total energy of the stage-2 GICs system, $E_{{\mathrm{FeCl}}_3}$ is the total energy of the $2\times 2$ units of layered FeCl${}_3$ primitive cell, and $E_{\mathrm{graphite}}$ is the total energy of $5\times 5$ units of AB stacking graphite (per unit cell containing two carbon layers).

3. Results

3.1. Structural Properties

As shown in Figure 1, two stacking patterns (AA stacking and AB stacking) and two magnetic configurations (ferromagnetic (FM) and antiferromagnetic (AFM)) were considered when performing the structural optimization of FeCl${}_3$-intercalated BLG. A supercell consisting of $5\times 5$ graphene primitive cell and $2\times 2$ layered FeCl${}_3$ primitive cell was constructed to reduce the lattice mismatch. During the optimization of the lattice parameter and structure, lattice constant c was fixed to 30 Å for the system to avoid the interaction between adjacent periodic structure.

Table 1. Calculated properties of graphene, BLG, graphite, FeCl${}_3$ monolayer, FeCl${}_3$-intercalated BLG and FeCl${}_3$-intercalated graphite: lattice constant a referring to $5\times 5$ graphene supercell (Å), energy of the system (eV), binding energy ($\Delta E_{\mathrm{bind}}$) or intercalation energy ($\Delta E_{\mathrm{int}}$) per two layers of $5\times 5$ graphene and one layer of $2\times 2$ FeCl${}_3$, magnetic momentum (${\mu }_B$), the average distance between C atomic layers (Å), the change in the z-coordinate of carbon atoms within both upper and lower carbon atomic layers (Å), and charge transfer occurring from graphene to FeCl${}_3$ (e).

Material	Stacking Pattern	Magnetic Configuration	Lattice Constant a (Å)	Energy (eV)	$\mathbf{\Delta }\mathit{E}$ (eV)	Magnetic Momentum (${\mathit{\mu }}_{\mathit{B}}$)	${\mathit{d}}_{\mathit{c}-\mathit{c}}$ (Å)	$\mathit{\Delta }{\mathit{d}}_{\mathit{c}-\mathit{c}}$ (Å)	Charge Transfer (e)
Graphene	-	-	12.339	−462.874	-	0.000	-	0	-
BLG	AA	-	12.337	−927.804	−2.056	0.000	3.656	0	-
	AB	-	12.336	−928.065	−2.308	0.000	3.486	0	-
Graphite	AA	-	12.337	−928.351	−2.604	0.000	3.621	0	-
	AB	-	12.336	−928.939	−3.120	0.000	3.485	0	-
FeCl${}_3$	-	FM	12.316	−122.800	-	40.000	-	-	-
		AFM	12.316	−122.817	-	0.000	-	-	-
FeCl${}_3$-BLG	AA	FM	12.331	−1053.586	−2.982	39.006	9.550	0.007/0.011	0.982
		AFM	12.332	−1053.571	−2.950	1.001	9.549	0.007/0.010	0.975
	AB	FM	12.332	−1053.579	−2.714	39.005	9.567	0.010/0.026	0.984
		AFM	12.332	−1053.572	−2.690	1.001	9.563	0.006/0.025	0.975
FeCl${}_3$-GIC	AB	FM	12.333	−2112.323	−4.422	78.001	9.510	0.005/0.035	2.003
		AFM	12.333	−2112.323	−4.405	0.000	9.510	0.005/0.035	1.985
		AFM2	12.333	−2112.357	−4.439	2.000	9.510	0.005/0.034	1.968

presents the calculated properties of FeCl${}_3$-intercalated BLG. The optimized lattice constant a was found to be approximately 12.33 Å for all the investigated structures, resulting in a lattice mismatch of 0.1% for graphene and 1.2% for FeCl${}_3$. Notably, FM configuration of FeCl${}_3$-intercalated BLG with AA stacking patterns exhibited the lowest energy. The binding energy ($\Delta E_{\mathrm{binding}}$) was calculated to be −2.98 eV, corresponding to an energy of −0.373 eV per FeCl${}_3$ unit, suggesting a favorable binding between FeCl${}_3$ and the graphene layers.

In terms of magnetic stability, the ferromagnetic (FM) state was found to be more stable than the antiferromagnetic (AFM) state for both AA and AB stacking, with energy differences of 15.2 meV and 7.4 meV, respectively. The distances between the two carbon atomic layers varied due to the different positions of Fe and Cl on the stacking carbon layers. It is noticeable that, for AB stacking, the AFM state exhibited slightly smaller $d_{c-c}$ values compared to the FM state, while the difference is not significant for AA stacking.

Furthermore, we investigated the structural changes in the system after intercalation by considering the FM alignment and AA stacking of FeCl${}_3$-intercalated BLG, as it exhibits lowest energy. Each Fe atom forms bonds with six Cl atoms, and the average Fe-Cl bond length around each Fe remains relatively unchanged compared to FeCl${}_3$ monolayer at approximately 2.42 Å. However, there is an exception for a specific Fe atom, where the average Fe-Cl bond length is enlarged to 2.48 Å. A distinct localization of electrons on this Fe atom is evident, gaining around 0.245 electrons. The detailed analysis of the electronic properties of the system will be discussed below.

As shown in Table 1, we quantified the changes in the z-coordinate of carbon atoms in the carbon atomic layers after the intercalation by calculating the difference between the highest and lowest z-coordinate values. The calculation results demonstrate that the intercalations yields a small buckling of the graphene layers, whereas the bending in the AB stacking is about doubly as large as for the AA stacking. Additionally, GIC exhibits even a larger change in the z-coordinate of carbon atoms compared to FeCl${}_3$-intercalated BLG.

3.2. Magnetic and Electronic Properties

The partial density of states (PDOS) and band structure of FeCl${}_3$-intercalated BLG were calculated using the PBE+U+D3 method. Figure A1 and Figure 2 depict the results of the density of states (DOS) for spin-up and spin-down components, respectively. The distinct separation between the spin-up and spin-down DOS peaks indicates a FM coupling in both AA and AB stacking configurations of FeCl${}_3$-intercalated BLG. This leads to a total magnetic moment of 39 ${\mu }_B$. Conversely, the DOS for the AFM configurations of FeCl${}_3$-intercalated BLG with both AA and AB stacking exhibit symmetric profiles, resulting in a total magnetic moment of 1 ${\mu }_B$. The states near the Fermi level predominantly originate from Fe 3d and Cl 3p orbitals.

The shift of the Dirac point can be observed for all structures with values of 0.737 eV for AA-FM, 0.682 eV for AA-AFM, 0.750 eV for AB-FM, and 0.676 eV for AB-AFM FeCl${}_3$-intercalated BLG. The bands near the Dirac points at the K point exhibit a distinct linear dispersion characteristic of the $\pi$ bands, which closely resembles that of single-layer graphene. Thus, we can conclude that the carbon atomic layers in FeCl${}_3$-intercalated BLG demonstrate similar electronic properties to those of single-layer graphene.

We further calculated the structural, electronic, and magnetic properties of stage-2 FeCl${}_3$-intercalated graphite, where adjacent graphene retains AB stacking as in pristine graphite is used for comparison, as it shows the same chemical formula C${}_{12.5}$FeCl${}_3$ with the FeCl${}_3$-intercalated BLG. We considered different magnetic configurations (see Table 1), and found that FM order within the FeCl${}_3$ layer and AFM order between the planes (named AFM2) has the lowest energy; therefore, we will discuss the electronic and structural properties only for this magnetic arrangement.

The optimized lattice constant a and c are equal to 12.333 and 26.032 Å, respectively. The distance between the two graphene layers is approximately 9.510 Å for the stage-2 GIC, which is somewhat smaller than the BLG by 0.04 Å. This result is expected, since in BLG, the graphene layers can relax to the vacuum region. FeCl${}_3$-intercalated graphite exhibits a more significant variation in the z-coordinate of carbon atoms compared to FeCl${}_3$-intercalated BLG. Additionally, in FeCl${}_3$ layers, a specific Fe atom shows an enlargement of the average Fe-Cl bond length, with a value of 2.48 Å, which is consistent with the behavior observed in the BLG system.The calculated intercalation energy is around −8.879 eV for the system, which corresponds to an energy of −0.555 eV per FeCl${}_3$ unit, which is significantly larger than in BLG. As shown in Figure 2c, the symmetric DOS suggest AFM coupling for stage-2 intercalated graphite and an up shift of the Dirac point of 0.695 eV can be observed on the band structure, which is slightly lower than for the BLG.

We further investigated the charge transfer between FeCl${}_3$ and carbon atomic layer of FeCl${}_3$-intercalated BLG and FeCl${}_3$-intercalated graphite. As shown in Figure 3, it is clear that the hole is delocalized within the graphene layers. The charge transfer in BLG (per FeCl${}_3$ layer) is slightly smaller than the stage-2 intercalated graphite, owing to the absence of the graphene layers on top and down side of the FeCl${}_3$-intercalated BLG. However, it is intriguing to note that the partial charges of the majority of Fe atoms remain largely unaffected, while a distinct localization of electrons on a specific Fe atom is evident, gaining approximately 0.245 electrons determined by the Bader analysis. Meanwhile, the 6 Cl atoms that bond with this Fe also undergo similar changes, gaining a total of 0.282 electrons, while the remaining 18 Cl atoms collectively gain 0.389 electrons (Figure 3a). Similar behavior is observed in FeCl${}_3$ GIC, where in each layer, one Fe atom gains 0.245 electrons, and the 6 Cl atoms bonded to this specific Fe gain a total of 0.273 electrons, while the remaining 18 Cl atoms collectively gain 0.405 electrons.

3.3. Pressure Dependence

Within the bilayer system, we can apply uniaxial pressure perpendicular to the 2D system to investigate whether the magnetic state can be modulated by pressure. As shown in

Table 2. Energies for FM and AFM states, shift of Dirac point, and charge transfer occurring from graphene to FeCl${}_3$ with varying interlayer distances for FeCl${}_3$ intercalated BLG.

${\mathit{d}}_{\mathit{C}-\mathit{C}}$ (Å)	${\mathit{E}}_{\mathit{F}\mathit{M}}$ (eV)	Shift of Dirac Point/  Charge Transfer Value	${\mathit{E}}_{\mathit{A}\mathit{F}\mathit{M}}$ (eV)	Shift of Dirac Point/  Charge Transfer Value
9.5	−1053.572	0.7579/0.9907	−1053.549	0.6919/0.9799
9.4	−1053.521	0.7648/0.9988	−1053.498	0.7021/0.9865
9.3	−1053.448	0.7666/1.0144	−1053.429	0.7065/0.9993
9.2	−1053.330	0.7734/1.0247	−1053.306	0.7180/1.0033
9.1	−1053.151	0.7740/1.0391	−1053.124	0.7249/1.0134
9.0	−1052.915	0.7753/1.0579	−1052.886	0.7259/1.0307

, we create the pressure by adjusting the interlayer spacing between the graphene layers while keeping the FeCl${}_3$ layer equally spaced from both. In the calculation, the z coordinates of the system were constrained, preventing relaxation along the vertical direction. However, the atoms retained the freedom to move within the xy plane, allowing for structural optimizations within that plane. The energy for both the FM and AFM states of FeCl${}_3$-intercalated BLG is determined at every interval of 0.1 Å when the interlayer spacing is changed from 9.5 to 9.0 Å.

Based on the calculation results, it can be concluded that in all studied structures, FeCl${}_3$-intercalated BLG exhibits greater stability in the FM state compared to the AFM state. The energy difference between the two states is approximately 25 meV for the system. This suggests that, even under pressure, the magnetic state of the FeCl${}_3$-intercalated BLG is independent of the pressure applied. The applied pressure increases the charge transfer and the shift of the Dirac point slightly, but the important finding is that not only the magnetic properties, but also the electronic properties, remain stable under applied pressure.

4. Conclusions

In summary, our calculations revealed that a distinct localization of electrons on a specific Fe atom is evident, gaining approximately 0.245 electrons, and its surrounding chlorides gain 0.282 electrons in total. The holes are delocalized within the carbon atomic layers with a positive charge of around 0.01 eV per carbon. Consequently, the intercalated graphene exhibits p-type doping, leading to a shift of the Dirac cone by 0.74 eV for BLG and 0.70 eV for stage-2 intercalated graphite. Moreover, our calculations indicate the presence of ferromagnetic ordering within the plane of FeCl${}_3$-intercalated BLG, while the FeCl${}_3$ layers in stage-2 intercalated graphite exhibit antiferromagnetic coupling. The ferromagnetic nature and the charge transfer remains stable under pressure. This stable high charge transfer from the carbon layers and the significant shift of the Dirac point, whereas the linear dispersion relations are preserved, suggests that FeCl${}_3$-intercalated BLG holds promising potential for future advances in low-dimensional electronics.